Evaluate express your answer in exact simplest form9P4=

Answer:

6. a because a rectangle with sides 8 and 2 has a perimeter of 20 but its area is 16.

7. d because 4 is an even number and it is a perfect square.

8. b because a pen can be used to write but is not a utensil.

Step-by-step explanation:

The solution to the system of linear equations 6 · x + 2 · y - 9 = 0 and y = 2 · x - 3 is (x, y) = (1.5, 0).

In this question we find a system of two linear equations and two variables, this can be done by using a Cartesian plane and drawing each line equation. The solution to the system is represented by the point of intersection of the two lines.

Therefore, the solution to the system of linear equations is (x, y) = (1.5, 0).

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The solution to the system of linear equations will be; 6x + 2y - 9 = 0 and y = 2x - 3 is; (1.5, 0).

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be one degree.

To solve a system of linear equations by graphic methods: we need a system of two linear equations and two variables, using a Cartesian plane and each line equation.

The solution to the system is shown by the point of intersection of the given lines.

6x + 2y - 9 = 0

y = 2x - 3

6x + 2 (2x - 3 ) - 9 = 0

x = 1.5

(x, y) = (1.5, 0).

Hence, the solution to the system of linear equations would be; (x, y) = (1.5, 0).

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Answer:

x = √213

I would appreciate this being marked as brainliest...

Step-by-step explanation:

This is a Pythagoras question because we are given two right-angled triangles and no internal angles other than the right angles.

That 7 is annoying because it won't form a Pythagorean triplet with 10. It means that the answer will probably be in radical form.

We can use radicals to represent the common side.

Introduce Pythagoras. The equation below forms a circle on a graph by the way where r is the radius of the circle.

a² + b² = c²;

Substitute the first triangle.

10² + 7² = c²;

100 + 49 = c²;

149 = c²;

c = √149;

Substitute the second triangle.

(√149)² + 8² = x²;

149 + 64 = x²;

213 = x²;

x = √213;

The leading term of the polynomial is [tex]4x^{3}[/tex] and the degree of the polynomial is 3.

A sheet of paper measuring 8.5 inches by 14 inches is currently in our possession. The box's volume V, measured in cubic inches, depends on the side length x, where V (x) = (14-2x)(8.5-2x)(x).

So, we have :

V (x) = (14-2x)(8.5-2x)(x)

[tex]V(x) = (14-2x)(8.5-2x)(x).\\V (x) = (14-2x)(8.5x-2x^{2} )\\V(x) = 4x^{3} -45x^{2} + 119x[/tex]

Thus, the leading term of the polynomial is [tex]4x^{3}[/tex] and the degree of the polynomial is 3.

Now, we have :
[tex]V(x) = 4x^{3} -45x^{2} + 119x\\V(x) = x ( 4x^{2} -45x +119)\\V(x) = x (x-7)(4x-17)[/tex]

Now, For intercepts, V(x) = 0

[tex]V(x) = x (x-7)(4x-17) = 0\\x (x-7)(4x-17) = 0\\\\x = 0, 7, 4.25[/tex]

Now when x = 0, V(x) =0

when x = 7, f(x) = 135

when x = 4.25, f(x) = 252.89

So, the points are (7, 135) and ( 4.25, 252.89)

These points represent the value of x and their corresponding value of V.

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Answer:

Slope = 3

Step-by-step explanation:

(-4, -10) and (-7, -19)

(x₁, y₁)           (x₂, y₂)

       y₂ - y₁        -19 - (-10)         -19 + 10        -9

m = ------------ = ---------------- = ------------- = -------- = 3

       x₂ - x₁          -7 - (-4)           -7 + 4           -3

I hope this helps!

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-10})\qquad (\stackrel{x_2}{-7}~,~\stackrel{y_2}{-19}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-19}-\stackrel{y1}{(-10)}}}{\underset{run} {\underset{x_2}{-7}-\underset{x_1}{(-4)}}} \implies \cfrac{-19 +10}{-7 +4} \implies \cfrac{ -9 }{ -3 } \implies 3[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-10)}=\stackrel{m}{ 3}(x-\stackrel{x_1}{(-4)}) \implies y +10= 3 (x +4) \\\\\\ y+10=3x+12\implies {\Large \begin{array}{llll} y=3x+2 \end{array}}[/tex]

Answer:

[a] 15

[b] 13

Step-by-step explanation:

       We can use the visual diagram given to solve. We can see that when you input -8 (on the left side) the arrow leads to the output 15, our answer.

       We use the same method for part b. When you input 3 (on the left side) the arrow points to 13 (on the right side) giving us an answer of 13.

To answer this question, we only need to replace x by 5, and then solve the resulting operations:

Therefore, the value for the expression 4x-13 when x = 5 is equal to 7.

The real world knowledge we use to understand the STEM task are :

A) STEM integrates it's concepts and applications to real life.

B) STEM helps in finding solution to the practical issues.

C) Focuses on building models and replicating scenarios.

What is STEM ?

STEM education refers to the integrated teaching and learning of the subjects such as science, technology, engineering, and mathematics.

We know that STEM teaches critical thinking skills and instills a passion for innovation. Beyond the advantages of learning STEM subjects, STEM supports the problem-solving and inquisitive learning that are essential for success in a range of tasks and professions. Colleges are now incorporating all of these helpful ideas into their normal study courses, and the results are clearly very favorable.

The real world knowledge we use to understand the STEM task is as follows :

Therefore , the real world knowledge we use to understand the STEM task are :

A) STEM integrates it's concepts and applications to real life.

B) STEM helps in finding solution to the practical issues.

C) Focuses on building models and replicating scenarios.

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Answer: Y = -2x + 1

Step-by-step explanation:

The line has a Y-Intercept of 1, shown as that's where the line passes the Y-Axis. The slope is negative 2, you can find such information by finding one point on a line, then making a triangle to the next point. In this case you would start at (0,1) and go right once (x axis) and down twice (y axis). The slope formula is y2-y1/x2-x1 or change in y/change in x, so if you put 2 (y axis) over 1 (x axis) you would have a slope of 2.

Answer:

5/8 and 25/64

The mean of the sampling distribution of sample means is 495 hours.

What is the mean of the samples?

The mean of samples is the average of a set of samples or data.

This can be calculated using the formula:

Mean= (Sum of terms)/(Number of terms)

Find the mean of each sample as shown below:

Mean service life of sample 1 = [tex]\frac{495+500+505+500}{4} = \frac{2000}{4}[/tex]

                                                = 500 hours

Mean service life of sample 2 =[tex]\frac{525 +515 +505 +515 }{4}=\frac{2060}{4}[/tex]

                                                  = 515 hours

Mean service life of sample 3 =  [tex]\frac{470 +480 +460+ 470}{4}=\frac{1880}{4}[/tex]

                                                  = 470 hours

Find the mean of the sampling distribution of sample means using the formula:

Mean of the sampling distribution (M)

=(Sum of mean of given samples )÷( Number of samples)

M = [tex]\frac{500+515+470}{3}=\frac{1485}{3}[/tex]

M=495 hours

So, the mean of the sampling distribution of sample means is 495 hours.

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The mean of the sampling distribution of sample means is 495 hours.

What is the mean of the samples?

The mean of samples is the average of a set of samples or data.

This can be calculated using the formula:

Mean= (Sum of terms)/(Number of terms)

Find the mean of each sample as shown below:

Mean service life of sample 1 = [tex]\frac{495+ 500+ 505+ 500}{4}=\frac{2000}{4}[/tex]

                                               = 500 hours

Mean service life of sample 2 = [tex]\frac{525+ 515+ 505+ 515 }{4}=\frac{2060}{4}[/tex]

                                                 = 515 hours

Mean service life of sample 3 =  [tex]\frac{ 470+ 480 +460 +470}{4}=\frac{1880}{4}[/tex]

                                                 = 470 hours

Find the mean of the sampling distribution of sample means using the formula:

Mean of the sampling distribution (M)

=(Sum of mean of given samples )÷( Number of samples)

M = [tex]\frac{500+515+470}{3}=\frac{1485}{3}[/tex]

M=495 hours

So, the mean of the sampling distribution of sample means is 495 hours.

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The equation y = 2/3x + 1  has a solution of (6, 5) and not (9, 8)

From the question, the equation is given as

y = 2/3x + 1

Also, we have the ordered pairs to be

(6, 5) and (9, 8)

For (6, 5), we have

x = 6 and y = 5

So, the equation becomes

5 = 2/3 x 6 + 1

Evaluate

5 = 5 --- true

For (9, 8), we have

x = 9 and y = 8

So, the equation becomes

8 = 2/3 x 9 + 1

Evaluate

8 = 7 --- false

Hence, (6, 5) is part of the solution and (9, 8) is not

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y = 6x is proportional.

Proportionality between x and y is defined if there is a constant of proportionality 'k' such that y = kx.

So here, the constant of proportionality in y = 6x is 6.

This equation also means that y varies directly with respect to x and then 6 is the constant of variation.

That is, y is directly proportional to x.

Then a change in y implies a corresponding change in x in the same direction as that of y.

If x increases, then y also increases and if x decreases, then y also decreases.

These changes are related to the constant of proportionality 6.

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Answer:

t = b+ c

total = bags + cartons

Answer- 3,315.53007332

Step-by-step explanation:

In this example the compounded is weekly, so the interest rate has to be converted to a weekly interest rate of tex2html_wrap_inline224 .

At the end of the first week, you will have the $1,000 you had at the beginning of the week plus the interest on the $1,000 or tex2html_wrap_inline226 . At the end of the week you will have

displaymath228

An expression that could represent the price of the item after the discount is 0.8y.

Given that, an item costs y dollars and then a 20% discount is applied.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Cost price = $y and Discount percentage = 20%

Discount = 20% of y

= 20/100 × y

= 0.2y

The price of the item after the discount = y-0.2y

= 0.8y

Therefore, an expression that could represent the price of the item after the discount is 0.8y.

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the red triangle is the building

the black triangle is the house

x is the height of the building

we have a problem of Tales triangles semblants so we can use this equalities

the height of the building is 110.5 feet

The values of x and XZ, calculated by the given equations are  3 and 30 respectively.

What is a equation?

The equals sign indicates that two expressions in an equation are equal. An equation is a mathematical formula. The meaning of the word equation and its cognates may change a bit depending on the language. An equation is defined as including one or more variables in French, as opposed to English, where an equation is defined as any well-formed formula that consists of two expressions connected by the equals sign.

Given information (and equations) in the question:

Y is between X and Z,

XY = 19,

YZ = 2x+5,

XZ = 6x+12

Since the question say Y is between X and Z, it means:

XY + YZ = XZ

Substituting the values in this equation by the values given in the question:

19 + 2x + 5 = 6x + 12

24 - 12 = 4x

x = 3

putting the value of x in the given equation:

XZ = 6x + 12

XZ = 6(3) + 12

XZ = 18 + 12

XZ = 30

Hence, the values of x and XZ are 3 and 30 respectively.

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Answer:

v = -16

Step-by-step explanation:

Move the variable to the left-hand side and change its sign, so it would then be -28 - v = -12

Then move the constant to the right-hand side and change its sign, so it would become - v = -12 + 28

Then you would calculate the sum: - v = 16

After doing so, change the sides on both sides of the equation, v = -16

So, your answer should be v = -16

Answer:

-2

Step-by-step explanation:

The line passes through the y-intercept at the point (0, -2)

Solution of Square root,  x² = 30: x = √30 = √30² = 30, x = -√30 = -√30² = 30

Solution of Cube root, x³ = 30: x = ∛30 = ∛30³ = 30, x = -∛30 = -∛30³ = -30

Given,

Square root x² = 30

Then, the value of:

x = √30 = √30² = 30

x = -√30 = -√30² = 30

x = ∛30 = ∛30² = 3.107

x = -∛30 = -∛30² = -3.107

Now,

Cube root, x³ = 30

x = √30 = √30³ = 164.317

x = -√30 = -√30³ = -164.317

x = ∛30 = ∛30³ = 30

x = -∛30 = -∛30³ = -30

Therefore,

Solution of Square root,  x² = 30:

x = √30 = √30² = 30

x = -√30 = -√30² = 30

Solution of Cube root, x³ = 30:

x = ∛30 = ∛30³ = 30

x = -∛30 = -∛30³ = -30

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Answer:

1 41/100

Step-by-step explanation:

Answer:

141/100 (Already in simplest form). As a mixed number, it is: 1 41/100

Step-by-step explanation:

Answer:

v=3.2

Step-by-step explanation:

12.8 = 4v

v= 12.8/4       isolate the variable and divide.

v= 3.2            Answer

⇒Vertical angles are equal .

This means that ∠1=∠2

⇒The trick is to first find the value of the unknown variable x then substitute it in the expression of ∠1 to get the exact magnitude of the angle.

[tex]5x+12=6x-11\\5x-6x=-11-12\\-x=-23\\\frac{-x}{-1} =\frac{-23}{-1} \\x=23[/tex]

x=23°

To get the exact value of ∠1 Plug in 23° in the place of x in the expression of ∠1:

[tex]< 1=5x+12\\=5(23)+12\\=127[/tex]

∠1=127°

Correlation is not sensitive to the scale of the data; however, covariance is  sensitive to the scale of the data, so the statement is false.

Covariance is a term used in statistic and regression analysis. Covariance shows how two variables differ.

Covariance is affected by the change in scale, for example if all the value of one variable is multiplied by a constant and all the value of another variable are multiplied, by the same or another constant all together, then the covariance is automatically changed.

Correlation is also a term used in regression analysis and statistics. Correlation shows how two variables are related and therefore not influenced by the change in scale.

Hence the given statement is False

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The values in order from least to greatest are 0-0.5,√(0.5),20%,20% √/0.5,√/0.5 |−0.5| 20%. we eliminate 0-0.5 because the value is two times in the option.

Percentage represents a proportion or a fraction of a whole, expressed as a portion of 100. It is commonly denoted by the symbol "%" (percent), which literally means "per hundred."

According to the given information:

The values in the list are:

0-0.5 = a range of values from 0 to 0.5, inclusive

√(0.5) ≈ 0.7071

20% = 0.2

20% √/0.5 = 0.2 * √(0.5) ≈ 0.1414

√/0.5 |−0.5| 20% = √(0.5) * |−0.5| * 0.2 ≈ 0.0707

Therefore, the correct list in order from least to greatest is:

0-0.5

√(0.5)

20%

20% √/0.5

√/0.5 |−0.5| 20%

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The probability that the student is a sixth-grader or rated good grades as most important is (168 / 335) + (135 / 335) = 0.904

Probability is used to determine the odds that a random event would happen. The odds that the event would happen lies between 0 and 1.

The probability that the student is a sixth-grader or rated good grades as most important = (number of sixth-graders / total number of students) + (students who rates good grades as most important / total number of students)

(168 / 335) + (135 / 335) = 303 / 335 = 0.904

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In probability , 5148 possible flushes in poker.

What is probability in math?

there are C(13,5) 5-card hands… i.e.

the number of combinations of taking 5 cards from 13 distinct cards.

But, since there are 4 suits, there are then 4*C(13,5) possible “flushes.”

Thus, there are 4*1287=5148 possible flushes in poker.

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The length of the radius of the circle is 44cm.

This problem bothers on the mensuration of flat shapes, a circular shape.

Given data

Circumference of circle C= 88πcm

Radius of circle r=?

To find the length of the radius of the circle.

To solve for the radius let us apply the formula for the circumference of a circle

C=2πr

Substituting our given data

88π=2πr

Making r subject of formula we have

r= 88π/2π

r= 44cm

Hence, The length of the radius of the circle is 44cm.

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